What is sqrt(1-((1-x^2)/(1+x^2))^2) ?

The solution to sqrt(1-((1-x^2)/(1+x^2))^2) is (2x)/(1+x^2)

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simplify sqrt(1-((1-x^2)/(1+x^2))^2)

simplify

1 - (\frac{1 - x ^{2}}{1 + x ^{2}})^{2}

\frac{2 x}{1 + x ^{2}}

Solution steps

1 - (\frac{1 - x ^{2}}{1 + x ^{2}})^{2}

Simplify

1 - (\frac{1 - x ^{2}}{1 + x ^{2}})^{2} : \frac{4 x ^{2}}{( 1 + x ^{2} ) ^{2}}

= \frac{4 x ^{2}}{( 1 + x ^{2} ) ^{2}}

Apply radical rule:

\frac{a}{b} = \frac{a}{b},

assuming

a \geq 0, b \geq 0

= \frac{4 x ^{2}}{( 1 + x ^{2} ) ^{2}}

Simplify

4 x^{2} : 2 x

= \frac{2 x}{( 1 + x ^{2} ) ^{2}}

Apply radical rule:

a^{2} = a,

assuming

a \geq 0

(1 + x^{2})^{2} = 1 + x^{2}

= \frac{2 x}{1 + x ^{2}}

(3 x + 7) (2 x + 6)

9 x^{2} + 54 x + 81

- 10 x - (8 x - 4 y + 2 z) + (5 x - 4 y - 2 z) - (10 x - 3 y - 4 z)

\frac{108}{12}

\frac{x ^{9}}{x ^{2}}

What is sqrt(1-((1-x^2)/(1+x^2))^2) ?
The solution to sqrt(1-((1-x^2)/(1+x^2))^2) is (2x)/(1+x^2)